Maybe it's a completely new and unknown kami. A kami created specifically for this fanfiction. This kami could have unique powers and a different view of the ninja world compared to the existing characters in Naruto. It would add a fresh and exciting element to the story.
Maybe it's an existing character from Naruto who has been elevated to Kami status. For example, Tsunade could be turned into a Kami, and Naruto's relationship with her could be a very different dynamic from their previous ninja - leader relationship. Or it could be Kaguya, who was already a very powerful being, and in this fanfiction, she reforms and becomes a Kami and Naruto's wife.
In fanfiction, the 'kami' could be an original deity created by the author. This new 'kami' could have its own motives and reasons for giving a gift to Naruto. Maybe it's a kami that has been observing Naruto's journey and decides to interfere to help him achieve a greater purpose. It could be a kami associated with nature, like a kami of the wind or the fire, and the gift could be related to that element.
Perhaps it could be a female version of an existing kami from Naruto lore. For instance, a female counterpart of the Sage of Six Paths. She would have vast knowledge and power, and her training of Naruto would be a way to pass on that ancient wisdom and strength.
Well, there might be characters from their clan. Since Itachi is from the Uchiha clan, other Uchiha members could play significant roles. They could be elders or other young Uchiha who are involved in the clan's affairs and in turn, affect Itachi and Izumi's story.
Their relationship would likely become more trusting. In marriage, they would have to rely on each other more. For example, Itachi might open up more about his missions and the secrets he has been keeping.
Their relationship could develop through mutual understanding. Naruto's open - hearted nature would help Izumi open up more. Izumi, in turn, would support Naruto in his duties as a village hero. They might start by sharing small things like their favorite foods and gradually move on to deeper conversations about their dreams and fears.
Maybe Jiraiya. Since Jiraiya was Naruto's mentor and taught him a lot of things. He might have some knowledge about summoning kami and pass it on to Naruto.
He would be super excited. Zuko would probably be right there on the floor with Izumi, coaxing her to take those first steps. He might hold out a small, shiny object from the Fire Nation as an incentive.
Yes, there are quite a few. You can start by looking on popular fanfic platforms like Archive of Our Own. Just search for 'ajin izumi and nakano' and you'll likely find a variety of stories with different themes and interpretations.